For maximal supergravity on Riemann-flat Bieberbach manifolds, the Kaluza-Klein spectrum can be reorganized so that all supertraces vanish up to mass power eight, yielding a finite, negative one-loop potential.
Quantum corrections to broken N = 8 supergravity
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We show that the one-loop effective potential of spontaneously broken N=8 supergravity is calculable and finite at all classical four-dimensional Minkowski vacua without tachyons in the spectrum. The reason is that the supertraces of the quadratic and quartic mass matrices vanish along the classically flat directions: Str M^2 = Str M^4 =0. We also show that Str M^6 = 0 but Str M^8 > 0 in a broad class of vacua with broken supersymmetry on a flat background, which includes all those explicitly identified so far. We find analytical and numerical evidence that the corresponding one-loop effective potential is negative-definite.
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Supersymmetry-breaking compactifications on Riemann-flat manifolds
For maximal supergravity on Riemann-flat Bieberbach manifolds, the Kaluza-Klein spectrum can be reorganized so that all supertraces vanish up to mass power eight, yielding a finite, negative one-loop potential.